Superposition

Ye are standing this day all of you before the Lord your God: your heads, your tribes, your elders, and your officers, even all the men of Israel, your little ones, your wives, and thy stranger that is in the midst of thy camp, from the hewer of thy wood unto the drawer of thy water; that thou shouldest enter into the covenant of the Lord thy God—and into His oath—which the Lord thy God maketh with thee this day. (Deut. 29:9-11) The above verses at the beginning of the Torah portion Nitzavim that is always read in the week preceding the Jewish New Year, Rosh HaShanah, are usually interpreted in terms of the unity of Jewish people: You are standing this day all of you [read: standing together in perfect unity]. This is not [...]

This they shall give, everyone who goes through the counting: half a shekel according to the holy shekel. Twenty gerahs equal one shekel; half of a shekel shall be an offering to the Lord Ex. 30:13 In this week’s Torah portion, Ki Tisa (Ex. 30), Jewish people are given the commandment of donating a coin as atonement, not just a coin – half a coin. But why half? If God thought, twenty gerahs would be too much, He could have commanded Moses to mint another coin worth ten gerahs. But no, the coin was to remain what it was—worth twenty gerahs—and Jews were to give half a coin. Don’t you find it peculiar? I don’t, because half-coins are my favorite metaphor when explaining entanglement to my physics students. What is entanglement? When obtaining [...]

As I wrote in my previous post, Schrödinger Menorah: Burning And Not Burning, the Lubavitcher Rebbe explains the miracle of Chanukah as a paradox of the menorah burning and not burning, thereby embodying the absolute nature of God, who is not limited by His infinity but combines all possibilities including infinitude (ko’ach bli gvul) and the finitude (ko’ach hagvul). The notion of the menorah burning and not burning easily lends itself to be cast in terms of the quantum superposition of states of burning and not burning. I couldn’t help myself to call it a Schrödinger Menorah. There a couple of problems, however, with this idea. Firstly, as the Rebbe wrote in 1971 in a letter to the editor of the Journal of the Association of Orthodox Jewish Scientists, “The idea of miracles implies [...]

The miracle of Chanukah revolves around a single-day-supply of olive oil burning for eight days during the rededication of the Holy Temple in Jerusalem (Bet HaMikdash), after Maccabees liberated Israel from the occupation by the Seleucid empire. There are countless explanations of the miracle of the oil lasting eight days. The Lubavitcher Rebbe offers a unique explanation. The Rebbe dismisses any explanation of the miracle that relies on the miraculous nature of the oil itself. The Rebbe maintains that to be kosher for the Menorah, the oil had to be natural olive oil, not some miraculous oil. According to the Rebbe, the miracle was that the natural oil was burning and not burning at the same time. The Rebbe draws an analogy with the dimensions of the Ark (Aron HaKodesh) in the Holy [...]

According to the Saadia Gaon, these two parshioth are really one parshah, which sometimes is split into two. In the language of Quantum Mechanics (QM) the two parshioth are entangled and have one state vector, i.e., they are described by the single wavefunction. Needless to say, this is not meant in a literal sense, as QM describes physical objects, whereas these biblical chapters are certainly not. Nevertheless, b’derech drush, we can loosely say that these parshioth are entangled, i.e., they are joint into one. These two Nitzavim and Vayelech speak of the opposite themes – “nitzavim” connotes standing( lit., you stand), while “vayelech” connotes walking (lit., …and he walked). As much as it seems paradoxical at first, from the physicist’s point of view, it is not surprising at all. Typically, entangled objects have [...]

Today was Rosh Chodesh Nissan (the New Moon – the beginning of the months of Nissan). There is a dispute in the Talmud as to when was the world created. According to Rabbi Eliezer, the world was created in the month of Tishrei. According to Rabbi Yehoshua, the world was created in the month of Nissan (Tr. Rosh Hashanah (10b)). The Chasidic thought attempts to reconcile these opinions suggesting that both opinions are correct—the world was created in Nissan in thought and Tishrei in deed. The problem with this approach is that for halahic (Jewish ritual law) purposes of calculating Jewish calendar, the planets are deemed to have commenced their heavenly orbits in Nissan, not in Tishrei! How could planets that haven’t been actually created yet start their orbital movements in Nissan?! This can [...]

In physics, we speak of systems and states. A system is a collection of physical objects (particles, waves, etc.). A system can be in various states. For example, a coin could have two states – heads and tails. A top also has two possible states – it can be spinning clockwise or counterclockwise. Light can have two states as well – being in the vertical polarization or horizontal polarization. In classical mechanics a system can only be in a pure state, i.e., at any given point in time, a coin can be either in a state “Heads” or the alternative state “Tales”. A top can be spinning either clockwise or counterclockwise, each of which is a pure state. In quantum mechanics, a system can be in a pure state or in a state [...]

When God created the first humans, Adam and Eve (Chavah), He created them as one. And God created man in His own image, in the image of God created He him; male and female created He them. (Gen. 1:27) Actually, as Midrash Rabbah (Gen. VIII:1) explains, Adam and Eve were created as one being as Siamese twins—attached by their side. When the story of the creation of Adam is repeated in the next chapter, it seems as a very different story: And the Lord God caused a deep sleep to fall upon the man, and he slept; and He took one of his ribs, and closed up the place with flesh instead thereof. And the rib, which the Lord God had taken from the man, made He a woman, and brought her unto the [...]

Today is Yud Tes Kislev -- Rosh HaShanah of Chasidut. Today I received two gifts, which I'd like to share. Lately, while learning Samach Vov, I've been struggling to understand the meaning of Sefirot Ein Keitz. Today, during shacharis shemone esreh, it donned upon me that the literal meaning of Sefirot Ein Keitz is infinite numbers. I suddenly realized that while Sefirot after the Tzimtzum are ordinary numbers, Sefirot before Tzimtzum—Sefirot Ein Keitz—are cardinal numbers developed by the mathematician Georg Cantor at the end of the 19 c. Later during the day, I got the second epiphany that Tzimtzum is the collapse of the universal wavefunction describing the creation. Before Tzimtzum, all creations were in the state of "yecholot" -- potentialities. After the Tzimtzum, i.e., after the collapse of the wavefuction, these potentialities actualized in specific [...]